Bose does not have LDAC, or even AptX, it's just AAC and SBC for now. They promised that AptX (Adaptive? not sure) would be coming early summer but it obviously hasn't happened yet, so for now it's just the two aforementioned codecs.
Also I'm not sure if I would say that Bose's ANC is MILES ahead of NTP, not in my opinion. Because I think the NTP's are among the best earbuds for ANC just behind the Bose -> Sony XM4's and maybe just a few others. It started out poor but after like one or two software updates it's been really good in my opinion.
But sure, the Bose QCII's are noticeably better, but it's not like a night and day difference. It's better at cutting out higher frequency-noises than the NTP but at the same time, without listening to music you will hear stuff anyway in LOUD environments. But based on your comment it sounds like you might have gotten a poor seal with the NTP's or something. But the Bose is still incredibly impressive and as good as you get with ANC in earbuds, and close to the best you can get even with on-ear headphones from all that I've heard from other people at least.
The difference in bass... well, I think the NTP's are "better" or at least more focused on the sub-bass response which is great even if it to me can sound slightly overdone (and toning it down in the app with the slider sort of makes the bass sound weird) with certain genres, but it's certainly impressive and sounds good.
The Bose also has a really impressive bass response to me, it's more mid-focused, but they've managed to tune it to a point where it sounds like it's slightly enhanced but in a frequency area maybe slightly above many earbuds who end up with the mid-bass bloat? This is subjective and will sound weird to many, but the bass in the QC's has this sort of "bouncy" and "rubbery" texture which makes it sound engaging as hell. They certainly have some sub-bass rumble to them as well, but it's not to the level of the NTP's.
The mids of the Bose are also nice in my opinion, vocals sound really good and forward with just a little bit of EQ. Highs might be the weakness of the earbuds, but that's not to say that it's bad. I think the main thing with the Bose is that it might not really be an audiophile sound, but it always makes music sound better than "good enough" to me, even poorer recordings. To me they're the definition of "inoffensive" but also not boring. I know somebody just over me said that they highs felt "overdone", not sure if that meant harsh, but to me there is NOTHING I have been able to do in the form of EQ:ing that have made the highs sound too harsh or sibilant FWIW. Might also be a fit-thing though.